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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Connectivity of Julia sets for Weierstrass elliptic functions on square lattices


Author: Joshua J. Clemons
Journal: Proc. Amer. Math. Soc. 140 (2012), 1963-1972
MSC (2010): Primary 37F10, 54H20; Secondary 37F20
Published electronically: September 27, 2011
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Abstract: We show that the Julia set of a Weierstrass elliptic function on a square lattice is connected. The techniques used to prove this result are used to show a similar result for a related family of rational maps obtained from the Laurent series.


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Additional Information

Joshua J. Clemons
Affiliation: Department of Mathematics, Phillips Hall CB#3250, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3250
Email: jclemons@vt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11079-7
PII: S 0002-9939(2011)11079-7
Received by editor(s): September 8, 2010
Received by editor(s) in revised form: January 24, 2011, and January 31, 2011
Published electronically: September 27, 2011
Additional Notes: This is part of completed Ph.D. work at the University of North Carolina under the supervision of Jane Hawkins
The author would like to thank the reviewer for the helpful suggestions that improved this paper.
Communicated by: Bryna Kra
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.